Some of the comparisons here were using distsqr when they should have been using dist. This resulted in "remove doubles" tool almost never removing doubles at the default tolerance.

While looking for paths to test the fix to each function, also found that automerge wasn't working because it only considered selected vertices, and is supposed to run after a transform to merge vertices that just moved (and are therefore selected), with vertices that were stationary during the transform (and are therefore deselected). Fixed by changing automerge to consider all vertices.